Subject: [mg85499] Re: Test for Irreducibility of certain polynomials with

From: dh <dh at metrohm.ch>

Date: Wed, 13 Feb 2008 04:05:25 -0500 (EST)

References: <fopa0n$afs$1@smc.vnet.net>

Hi Guillermo,
how can you determine if a polynomial is irreducible if the coefficients
are unknown? It seems to me that you have to specify d before you can
say if it is irreducible.
hope this helps, Daniel
Guillermo Pineda Villavicencio wrote:
> Hi there,
>
> I want to test the irreducibility of the following polynomials of
> degree r with Mathematica.
>
> H[x_,d_] := Sum[(-d + 1)^(j)*Binomial[r - j, j]*x^(r - 2*j), {j, 0, (r -
> 1)/2}]
>
> I use the Mathematica function
>
>
> IrreducibleQ[p_?PolynomialQ,Modulus->m_]:=Module[{f=FactorList[p,Modulus->m]},
> Total[Last/@DeleteCases[f,{_Integer,_Integer}]]==1
> ]
>
> But I want Mathematica to consider H[x,d] as a function in x (not in x
> and d). Is it possible???
>
> Best regards,
> Guillermo
>